Aims. With its high sensitivity, the pyramid wavefront sensor (PyWFS) is becoming an advantageous sensor for astronomical adaptive optics (AO) systems. However, this sensor exhibits significant non-linear behaviours leading to challenging AO control issues.

Methods. In order to mitigate these effects, we propose to use in addition to the classical pyramid sensor a focal plane image combined with a convolutive description of the sensor to fast track the PyWFS non-linearities, the so-called optical gains (OG).

Results. We show that this additional focal plane imaging path only requires a small fraction of the total flux while representing a robust solution to estimating the PyWFS OG. Finally, we demonstrate the gain that our method brings with specific examples of bootstrapping and handling non-common path aberrations.